Some great granite bouldering and soloing to be had on Dartmoor - 2.5 to 3hrs from London (depending where in London you are? I think). Easy to camp and doss too - good scenery and pretty chilled out...pubs around, cream teas and pretty concentrated etc. Certainly keep you busy for a few days...verging on esoteric...Never been to Peak so no comment! But crowded apparently? Prob at least a good 4 hours from London to N.Wales (again depends where u r in the smog?) I'd probably choose there for the variety and choice and just to have said I've been there....(bouldering, long mountain days out, atmospheric, solitude if wanted). Easy to camp and doss, pubs etc. Campsite opposite the Vaynol in Llanberis Pass is convenient. There are also several Hut style thingies in the pass...have a search around. Have a couple of plans and see what the weather's doing!
PS unless u r old skool you'll prob need a pad in N.Wales..prob not in Dartmoor as most of the landings are better I reckon...and it's a lot easier to doss. Dartmoor will have tourists but not so much fleece where NWales will be covered with both. I reckon Dartmoor - just for the no hassle factor..plus you can always do some DWS (limestone) on the Torbay coast and get to Cornwall. Leave NWales for when you have more time!